Related papers: On some asymptotically flat manifolds with non max…

In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped…

In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay…

Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for…

In this work we present a "modest" holographic reconstruction of the bulk geometry in asymptotically flat spacetime using the two-point correlators of boundary quantum field theory (QFT) in asymptotically flat spacetime. The boundary QFT…

Almost-isometries are quasi-isometries with multiplicative constant one. Lifting a pair of metrics on a compact space gives quasi-isometric metrics on the universal cover. Under some additional hypotheses on the metrics, we show that there…

We find constrained instantons in Einstein gravity with and without a cosmological constant. These configurations are not saddle points of the Einstein-Hilbert action, yet they contribute to non-perturbative processes in quantum gravity. In…

The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation…

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank~1. This conjecture has been proved by Z. Szab\'{o} \cite{Sz} for harmonic manifolds with compact universal cover. E. Damek…

We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to $\R^{n}\setminus \Omega, n\ge 3$, and so that their boundary is a minimal hypersurface. (Here, $\Omega\subset \R^{n}$ is open…

We prove the existence of compact surfaces with prescribed constant mean curvature in asymptotically flat and asymptotically hyperbolic manifolds. More precisely, let $(M^3,g)$ be an asymptotically flat manifold with scalar curvature $R\ge…

We study solutions to the Kapustin--Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing…

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action…

In this paper we derive a precise estimate on the growth of potential functions of complete noncompact shrinking solitons. Based on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume…

We prove that the only smooth, Ricci flat, ALE instanton with a toric Hermitian non-K\"ahler structure is the Eguchi-Hanson instanton. The proof is analogous to the classification of toric Hermitian ALF instantons by Biquard and Gauduchon,…

It is shown by Colding and Minicozzi the uniqueness of the tangent cone at infinity of Ricci-flat manifolds with Euclidean volume growth which has at least one tangent cone at infinity with a smooth cross section. In this article we raise…

Let $(M,g)$ be an asymptotically flat Riemannian manifold of dimension $n\geq 3$ with positive mass. We give a short proof based on Lyapunov-Schmidt reduction of the existence of an asymptotic foliation of $(M, g)$ by stable constant mean…

We study the volume growth of hyperkaehler manifolds of type $A_{\infty}$ constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact complete 4-dimensional hyperkaehler manifolds of infinite topological type. These manifolds…

Asymptotically locally AdS and asymptotically flat black hole solutions are found for a particular case of the Horndeski action. The action contains the Einstein-Hilbert term with a cosmological constant, a real scalar field with a non…

We give an original analytic construction of hyperkahler ALF metrics on some ALE spaces of dihedral type, namely the spaces corresponding to minimal resolutions of Kleinian quotients relative to some binary dihedral group.

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…